Reliability Engineering

Common-Cause Failure Adjusted Minimal Cut Set Probability (Binary, Inclusion-Exclusion with Alpha Factor) calculator

Common-Cause Failure Adjusted Minimal Cut Set Probability (Binary, Inclusion-Exclusion with Alpha Factor) engineering calculator.

Runnable This tool can run, but independent engineering verification has not been established.

Quick Answer

Calculate Common-Cause Failure Adjusted Minimal Cut Set Probability (Binary, Inclusion-Exclusion with Alpha Factor)

Calculator

Top event probability (dimensionless)
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Result Interpretation

Common-Cause Failure Adjusted Minimal Cut Set Probability (Binary, Inclusion-Exclusion with Alpha Factor) calculator computes Top event probability in dimensionless using the defined engineering formula and the input values provided. Top event probability is expressed in dimensionless. No universal acceptance threshold is defined by this calculator.

Worked Example

Verified calculation

Given:

  • Basic event failure probability (common-cause mode) = 0.002
  • Basic event failure probability (independent mode) = 0.0005
  • Number of basic events in common-cause group = 2
  • Number of basic events in independent group = 3
  • Alpha factor (fraction of failures attributable to common cause) = 0.05

Expected Result:

  • Top event probability = 0.0016240876187499

Engineering Interpretation:

Under the given input conditions, the calculated result is: Top event probability = 0.0016240876187499 dimensionless.

The actual numerical result is computed by the Runtime engine using the persisted tool definition. The values shown here come from deterministically validated test cases.

Formula / Method

top event probability = 1 - pow(1 - fraction of failures attributable to common cause * (1 - pow(1 - common-cause mode, number of basic events in common-cause group)) - (1 - fraction of failures attributable to common cause) * (1 - pow(1 - independent mode, number of basic events in independent group)), 1)

Formula family: formula_reliability_fault_tree_minimal_cut_set_probability_calculator_binary_dependent_events_with_common_cause

Variables

SymbolLabelRoleDescription
p_b Basic event failure probability (common-cause mode) INPUT Basic event failure probability (common-cause mode)
p_i Basic event failure probability (independent mode) INPUT Basic event failure probability (independent mode)
n_b Number of basic events in common-cause group INPUT Number of basic events in common-cause group
n_i Number of basic events in independent group INPUT Number of basic events in independent group
alpha Alpha factor (fraction of failures attributable to common cause) INPUT Alpha factor (fraction of failures attributable to common cause)
result Top event probability OUTPUT Top event probability

Calculation Steps

  1. Enter the basic event failure probability (common-cause mode) in dimensionless.
  2. Enter the basic event failure probability (independent mode) in dimensionless.
  3. Enter the number of basic events in common-cause group in dimensionless.
  4. Enter the number of basic events in independent group in dimensionless.
  5. Enter the alpha factor (fraction of failures attributable to common cause) in dimensionless.
  6. Step 1: Compute top event probability.
  7. Read the top event probability (dimensionless) from the results.

Engineering Summary

Calculate Common-Cause Failure Adjusted Minimal Cut Set Probability (Binary, Inclusion-Exclusion with Alpha Factor)

Frequently Asked Questions

What does this calculator calculate?

The Common-Cause Failure Adjusted Minimal Cut Set Probability (Binary, Inclusion-Exclusion with Alpha Factor) calculator estimates Top event probability based on the input parameters you provide

Why is basic event failure probability (common-cause mode) important in this calculation?

basic event failure probability (common-cause mode) is used directly in the calculation of top event probability. Its effect on the result depends on the complete formula and the values of the other inputs.. When you enter basic event failure probability (common-cause mode) in dimensionless, the calculator uses it in the engineering formula to compute the output

How should I interpret the result top event probability?

The calculator outputs top event probability in dimensionless. The result is computed directly from the input values using the defined engineering formula

What units should I use for the inputs?

Enter each value in the units shown next to the input field: Basic event failure probability (common-cause mode) (dimensionless), Basic event failure probability (independent mode) (dimensionless), Number of basic events in common-cause group (dimensionless), Number of basic events in independent group (dimensionless), Alpha factor (fraction of failures attributable to common cause) (dimensionless). Make sure all inputs use the specified units for consistent results

What assumptions does this calculator use?

This calculator uses automatically validated engineering formulas. Results are approximate and should be validated against site-specific conditions, applicable codes, and professional engineering judgment

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